Hybrid seminar at McGill University or Zoom.

Large agent networks pose strong mathematical and computational challenges due to the high number of agents and the complex topologies between them. Mean field games (MFGs) and mean field control (MFC) provide a way to model large agent populations in a conceptually elegant way and also enable the design of efficient learning algorithms for large agent populations. While the seminal graphon MFG approach has extended the MFG idea to dense graph sequences with simple edges, this talk aims to introduce models which combine the MFG principle with complex edge types and sparse graphs. The first part of this talk will be about colored digraphon mean field games which leverage colored digraphons to allow for weighted, directed and time adaptive interactions between agents. Subsequently, it will be discussed how to extend MFGs and MFC to topologies with different levels of sparsity by using the concepts of Lp graphons, graphexes and especially locally weak converging graph sequences. The talk will complement the presentation of theoretical results with illustrative examples and numerical evaluations for different problem scenarios on synthetic and empirical networks.

Bio: Christian Fabian is a Ph.D. student in the Self-Organizing Systems Lab led by Prof. Heinz Koeppl at Technical University Darmstadt and his research is supported by the Hessian Center for Artificial Intelligence (Hessian.AI). Prior to joining TU Darmstadt, Christian received a B.Sc. in Economics and Business Administration (2017), a M.Sc. in Quantitative Finance (2020) and a B.Sc. (2019) and M.Sc. (2021) in Mathematics from Goethe University Frankfurt. His current research aims to understand large agent networks by combining mean field games with graph theoretical limiting concepts and to learn approximate equilibria in the resulting systems.